The Rational Zero Theorem states that the possible rational zeros of a polynomial function are all the possible ratios of factors of the constant term to factors of the leading coefficient. In this case, the constant term is 6 and the leading coefficient is 4. Therefore, the possible rational zeros of the function f(x) = 4x³ - 5x² + 2x + 6 are all the possible ratios of factors of 6 to factors of 4. These possible rational zeros are:
±1/4, ±3/4, ±1/2, ±3/2, ±1, ±2, ±6
To find out if any of these possible rational zeros are actual zeros of the function, we can use synthetic division or long division to divide the function by each possible zero.